A Single Statistic for Monitoring the Covariance Matrix of Bivariate Processes

ABSTRACT

In this article, we present a new control chart for monitoring the covariance matrix in a bivariate process. In this method, n observations of the two variables were considered as if they came from a single variable (as a sample of 2n observations), and a sample variance was calculated. This statistic was used to build a new control chart specifically as a VMIX chart. The performance of the new control chart was compared with its main competitors: the generalized sampled variance chart, the likelihood ratio test, Nagao's test, probability integral transformation (v _t ), and the recently proposed VMAX chart. Among these statistics, only the VMAX chart was competitive with the VMIX chart. For shifts in both variances, the VMIX chart outperformed VMAX; however, VMAX showed better performance for large shifts (higher than 10%) in one variance.

KEYWORDS:

• bivariate processes
• control chart
• variance monitoring

ACKNOWLEDGMENTS

The authors acknowledge the anonymous reviewers for their suggestions that greatly contributed to this article. We also thank CNPq for partial financial support of this research.